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(C) In a standing wave, the displacement of any particle at position $x$ is given by $y(x, t) = A(x) \sin(\omega t + \phi)$.All particles in a given l

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in one time period all the particles are simultaneously at rest twice.

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(C) In a standing wave, the displacement of any particle at position $x$ is given by $y(x, t) = A(x) \sin(\omega t + \phi)$.All particles in a given loop oscillate with the same phase, but particles in adjacent loops oscillate with a phase difference of $\pi$.At the extreme positions, all particles in a specific loop reach their maximum displacement simultaneously.However, because adjacent loops are out of phase, when particles in one loop are at their positive extreme, particles in the adjacent loop are at their negative extreme.Thus, all particles in the string are never at their positive extremes simultaneously.Conversely, all particles pass through their mean position (where they are momentarily at rest in terms of displacement, though velocity is maximum) twice in one time period $T$.Specifically, at $t = 0, T/2, T, \dots$, the entire string is momentarily straight (displacement $y = 0$ for all $x$).Therefore, in one time period, all particles are simultaneously at rest (at their mean position) twice.

In a standing wave on a string rigidly fixed at both ends:

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